So I can see this being tricky for game balance purposes, but I was considering the possibilities of having upgrades for pastures to auto-breed animals. No idea which tech to tie it to, maybe one of the further along alchemy ones to keep it from being too easy early-game.

Obviously they'd need to be supplied with the necessary food, but maybe to make it more of a trade off, they could require some kind of crafted wheat or otherwise more valuable resource (alchemy type stuff maybe? glistering melons? ) to auto-breed with. That way players have to balance the added cost of auto-breeding to the time saved by not having to sit there doing it manually.

And of course, mob limits still apply. And to limit it further, maybe you'd have to designate a pasture for a single type of animal to auto-breed (by buying the appropriate upgrade, thus locking out other options a la the store, library, etc)

I'm really just spit-balling here, this could be a terrible idea altogether for some reason, and there's all kinds of decisions to be made regarding game balance, but its a starting point.